So I have this idea for a gun; it's a normal gun, but it has an underbarrel attachment that fires a harpoon. Normally, the harpoon can be used just as a bayonet, but it has the added benefit of being fire-able. The harpoon can be attached to a rope if desired, or just fired and forgotten.
What I'm wondering is if the harpoon can pierce modern body armor. How fast would it have to be going, what kinds of forces would it take, and how big/powerful would the resulting firing mechanism have to be?
I'd like the harpoon to be re-fireable, so anything that can fire it multiple times would be preferable. Also, I'd like the firing mechanism to be sort of small, at least small enough to be carried by a normal human. The gun need not be pneumatic, nor does it need to resemble an actual harpoon gun, so long as the projectile is vaguely reminiscent of a harpoon (a long metal rod with a pointy bit at the end).